Graph Minors. XI. Circuits on a Surface

Neil Robertson, P. D. Seymour

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


Let Γ be a graph or hypergraph drawn on a connected surface which is not a sphere, in such a way that every non-null-homotopic curve meets the drawing at least θ times. We show that this defines a “tangle of order θ” in Γ, in the sense of earlier papers of this series. Also, there is a natural distance function defined by the drawing, and we show that for any point c of the surface, and any θ′ > θ, the set of points within distance θ′ of c is simply-connected.

Original languageEnglish (US)
Pages (from-to)72-106
Number of pages35
JournalJournal of Combinatorial Theory, Series B
Issue number1
StatePublished - Jan 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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